Subwoofer Design Theories

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Sealed - 2nd Order Acoustic Suspension

Basic Theory

The driver is mounted in a sealed, airtight enclosure, generally with the front of the driver facing outward but is not restricted to this method only.  The volume of the enclosure is chosen to achieve a desired system Q which defines the response characteristics of the driver and enclosure.  Q values may range between the 0.5 and 1.5 - with 0.5 being overdamped, 1.5 being underdamped, and 0.7 being critically damped or flat.   The total system Q (also known as Qtc) is dependent on 3 things: the volume of enclosure, the T/S parameters of driver and internal treatment compounds.  A a general rule only, sealed enclosures may be best suited for drivers with an EBP (Efficiency Bandwidth Product) of 50.0 or lower and drivers with Qts values above 0.40 but is not restricted to these exact values.  EBP is calculated by taking the the fs of the driver and dividing it by the Qes - therefore EBP = fs/Qes.  The cutoff rate is typically 12 dB/octave below f3, however higher system Q's result is a somewhat sharper roll-off (~14 dB/octave) while lower system Q's result in a slightly more shallow roll-off (~10 dB/octave).  Better damping and better transients are achieved by shooting for a lower system Q which can be accomplished by either making the enclosure larger or by adding stuffing/damping material.  Suitable damping materials include polyfill, Dacron, fiberglass, and acoustic foam.  Box stuffing will also affect f3 by either raising it or lowering it depending upon the type and amount of stuffing used.  Stuffing makes the box "appear" to be acoustically larger than it really is.

Advantages

2nd order sealed enclosures are simple to design and offer outstanding performance in a wide variety of applications.  They are easy to model with software and get predicted results.  Box size and shape are generally the least complex.  Great for both beginning and advanced DIY’ers.  The exact desired response characteristics can be achieved by simply designing for a particular Qtc (or system Q).  Modeled performance is easily altered by varying the size of the enclosure and/or the amount of stuffing material used.  They exhibit a very shallow cutoff rate of 12 db/octave below fB.   This results in much better group delay response.   Fast, quick, natural, smooth, tight, accurate, controlled and warm are some common subjective terms one might use to describe sealed enclosures.   Transient response is the best of all enclosure types.  The excursion of the driver increases as the frequency applied decreases until fB is reached after which the driver excursion begins to decrease.  There is typically no need for subsonic filtering due to the enclosure’s natural tendency to inhibit extremely low frequencies.  This results in less bottoming out of drivers at subsonic frequencies.  However, this only applies for smaller enclosures.  As the enclosure size gets larger, more Xmax is required in order to prevent overexertion for the same amount of input power.  Sealed enclosures have more extended low frequency response than vented enclosures given the same f3 for both due to the shallower rate of roll-off.  Phase shift is minimal within its normal operating frequency range. 

Disadvantages

Very low frequency output is difficult to achieve without active filtering.   The f3 (also know as 3dB down point) is usually fairly high, above 30 Hz in most applications and by simply increasing Vb, one cannot lower f3 for any given driver.  Low f3's in a sealed enclosure can be achieved by using drivers with a very low free air resonance or Fs.  Less power efficient by about -3 dB as compared with vented enclosures.  Lower over SPL capabilities.  There's a strong need for drivers with a very large Xmax in order to ensure safe operation at least down to fB, especially if the box is designed for Qtc values < 0.7  Any enclosure volume that is modeled with the system Q larger than 0.707 results in higher f3.  Lowest f3 is achievable only under an ideal Q = .707 alignment which may require unusually large and sometimes undesireable enclosure volumes.

Best Applications

Best suited where a completely uncompromised sound quality is desired.  Best for classical music and most rock and pop type music.  Most widely used in car stereo systems where cabin gain can make up for its lack of low end <30Hz bass.  Where size is an issue.  Sealed boxes can be half the size of vented boxes yet can be made even smaller if a higher Q is allowed.  May also be use for small to moderately sized Home Theaters.  Usually is the easiest box to pass SAF (spouse acceptance factor).  You should also go with sealed when the driver's T/S parameters dictate that the driver should be housed in a sealed enclosure due to a high Qts (above 0.4) or an EPB of 50 or lower - though this just a guideline and not a rule.

Ported - 4th Order Vented

Basic Theory

Also known as bass-reflex, ported or vented.  The driver is mounted into an enclosure which houses a large opening, port, vent or slot that extends into the cabinet a specified length.  The length and area of this vent are extremely critical to the proper function of a 4th order enclosure.  The port and driver contribute together to provide the desired response characteristic.  The driver is generally mounted with the front facing outwards, but is not restricted to this method only.  The vent which extends into the cabinet tunes the enclosure to a specific frequency (known as fB) thereby acting as a high pass filter on the driver.  Driver excursion is at its minimum at fB where the vent then takes over and provides most of the output.  Cut-off rate below fB is 24 dB/octave but can be varied up or down 5-6 dB depending upon the exact tuning frequency and volume of the enclosure.  There are various types of alignments that all fit into the ported 4th order category.  Some common types are QB3, EBS, SBB4 and SC4.  By varying the enclosure size and the tuning frequency, it is possible to achieve a variety of distinct low- frequency performances from a single driver.  The vent acts by damping the load produced by the driver above fB causing it to behave somewhat as if it were in a sealed enclosure.  Best suited for drivers with an EBP near 100.0 or higher and Qts < 4.0 but is not restricted to these numbers only.
Advantages Extended low frequency response.  3 dB down points (f3) are capable of being near or even below 20 Hz.  Increased power handling above fB due to reduced driver excursion at and while nearing fBMore efficient system.  Generally +3dB increased output over sealed enclosures due to the combined output of driver and port.  More overall SPL capabilities.  Deep, powerful, full, loud, inspiring, incredible, and earth shattering are common subjective terms associated with vented enclosures. 
Disadvantages

Larger enclosure size.  More difficult to accurately achieve predicted results.  Misaligned enclosures can result in very poor bass quality.  Very accurate T/S parameters of actual driver is required.  Although sometimes you can get away with using manufacture’s specifications.  Driver unloading or bottoming out below fB is very common.  Xmax is reached easily below fB and may cause sever damage the the driver's suspension, voice coil or cone.  This usually requires the need to install additional high pass filtering below fB.  But is not a always a necessity as long as power levels and frequency content are kept within reason.  Transient response is degraded, yielding typical group delay curves as high as 50 ms.  Muggy, boomy, sluggish, one-note, slow, and inaccurate are common subjective terms associated with vented enclosures.  Port diameter must be large to avoid unwanted port noise, which in turn requires the port to be long for any given Fb, which then drives up the volume of the enclosure, sometimes to undesirably large proportions.  Port chuffing if port area is not kept in check.

Best Applications Where the deepest and loudest bass is necessary.  Where size is not a huge issue but may still be a definite factor.  For Home Theater and music.  May be best suited for sound reinforcement, theater, live performances, DJ and other situations where lots of loud deep bass is needed and transient response is less critical.

 Bandpass - Dual Chamber Vented/Sealed 4th Order

Basic Theory

The front and the rear of the driver are housed in their own separate and distinct enclosures.  The front of the driver is in a ported enclosure while the rear of the driver is in a sealed enclosure.  The driver may be mounted the other way around however as long as one chamber is sealed while the other is vented.   The enclosure is designed as a sealed enclosure but with the addition of an acoustic filter (the port) in series with the front of the driver that acts to limit the driver's bandwidth and therefore increase its SPL capabilities within its bandwidth.
Advantages Very low f3 is possible at the expense of lower efficiency and increased ripple.  Extremely high SPL is also possible at the expense of a higher f3 and narrower bandwidth.  Less overall driver excursion.  More control over cone movement.  Bandwidth and efficiency are inversely proportional.
Disadvantages Combined volume of both chambers results in large overall enclosures.  Difficult to design properly.  Results may vary substantially due to misalignment of both front and rear chambers as well as tuning frequency.  Tend to have "one-note" bass, especially if designed or built poorly.   In order to achieve a wide useable bandwidth, there must be some amount of mid-band ripple as well as decreased efficiency.  Drivers can be easily blown due to high compression factors because of lowered cone motion and thereby exceeding the thermal limits of the driver before exceeding its mechanical limits.  Bandwidth and efficiency are inversely proportional.
Best Applications Where the large size of enclosure is of little concern.  In cars where the design calls for high SPL where the limited bandwidth which results can be increased due to cabin gain.  The cabin gain will help achieve a flatter and wider bandwidth across the desired range while maintaining the increased SPL of the enclosure.  Very popular in car applications for this reason.

Bandpass - Dual Chamber Vented 6th Order

Basic Theory

 

The front and rear of the driver are mounted in separate enclosures and tuned to specific calculated values.  Resultant output is suppose to be better than any of the other designs mentioned previously.   Bose owns the rights to the exact details behind this design.  They explain the theory like this, "The low-frequency speaker drivers are located between separate acoustic compression chambers inside a patented Bose Acoustimass module. As each speaker cone moves, it excites air in the chambers. Trapped in the chamber, this air acts as an acoustic spring, which interacts with the air in the port to produce more low-frequency sound with less power.  The system is more efficient and requires less cone motion, which in turn produces less distortion. In the event that any otherwise audible distortion is produced, the patented design traps it inside the acoustic chambers -- so it never enters the room. The result is an Acoustimass module with no audible distortion that can be located anywhere in the listening area."  www.bose.com
Advantages

 

More efficient system within its bandpass.  More control over cone movement.   Less audible distortion.  This doesn't necessarily mean that there is a true reduction in distortion from the driver, but that any distortion that is present form the driver can't be heard as well due to the chambers acting as filters on any unwanted noise.  My opinion only.
Disadvantages

 

Combined volume of both chambers may result in large overall enclosures.  Very difficult to design properly.  You may have to experiment a great deal before getting this design to sound acceptable.  Results may vary substantially due to misalignment of both front and rear chambers as well as tuning frequency of each chamber.   Drivers can be easily blown due to high compression factors because of lowered cone motion and thereby exceeding the thermal limits of the driver before exceeding its mechanical limits.  The driver may in fact tear itself to pieces.   There are no exact parameters or calculations for designing 6th order bandpass enclosures due to the patent owned by Bose.  So if you build one, you're basically on your own.
Best Applications

 

For more information on 6th order bandpass enclosures please visit www.decware.com

EBS - 4th Order Large Vented Enclosure with Low Tuning

Basic Theory

 

EBS- Extended Bass Shelf.  This is only one of the various different types of vented alignments which are possible and follows many of the same characteristics of vented enclosures.  The idea is to intentionally design the enclosure to be 125-175% larger than the optimal calculated volume and then tune the enclosure much lower than optimal as well.  The result is a significant amount of extended low frequency response.  When the response curve is simulated, a visible "shelf" can be seen in the curve just above the tuning frequency before it sharply rolls off.  The LEAP manual explains EBS theory like this: "The name [EBS] was derived simply from the visible appearance of the response curve. The bass response is extended to a lower frequency than would be possible from the QB3 alignment, but at a lower level or shelf relative to the mid band level. Although the EBS alignment is not a nice neat flat alignment such as the QB3, it is very often a much better choice than the QB3. The EBS alignment has some interesting features. Consider a loudspeaker with a Qts of 0.30, the QB3 alignment would have about 2dB more output at a frequency of twice the Fs, while the EBS alignment would have over 2db more output at Fs.  In most cases the EBS alignments will have far more subjective [low] bass than the QB3 alignments. Also, if you were to equalize the responses flat to Fs, 10db more boost would be required for the QB3 versus the EBS. This can dramatically consume large amounts of headroom in the power amplifier, and may also far exceed the linear excursion limits of the speaker.  The EBS alignment will maintain much lower cone excursion at frequencies near Fb than is possible with the QB3 alignment. This can be very important for high power systems." 
Advantages

 

Extended low frequency response down into the teens.  Subsonic, earth-shattering bass response.  Increased efficiency at the lower frequencies (below ~25 Hz) but decreased efficiency at higher  frequencies (above ~30 Hz) depending on tuning and box volume.  This is a rough figure since many different combinations can be designed to yield specific results.   In general, low frequency is extended and efficiency increased at the expense of reduced efficiency at higher frequencies - all within the generally accepted range known as bass. 
Disadvantages

 

The enclosure size is huge.  Anywhere from 5-15 cubic feet depending on the size of the driver being used.  Power handling capability of driver is reduced anywhere from 25-50%.  Driver may reach Xmax sooner above fB even if it never reaches Xmax right at or below fB.  Lack of real presence, lack of kick or punch, may be subjective terms uses to describe EBS alignments.  The overall impact of the bass is much softer.  Signals between 40 and 60 Hz are reduced.  Harder to "sell" because most people are more receiving to a pronounced upper bass response rather than an incredibly low and deep bass response .  It takes 8 times as much power (as well as moving air) to make 20 Hz sound as loud as 40 Hz.
Best Applications

 

Where the truly deepest of all heavenly deep bass is desired.  For drivers with a large Xmax and the ability to consume large amounts of power.  For drivers whose T/S parameters dictate an optimal enclosure size that's smaller than what the designer wants to build.  Large Home Theaters and varying kinds of music with heavy bass tracks would take the best advantage of this enclosure alignment.  Where size is no concern and sub-20 Hz bass is the main goal.  Bragging rights.

PR - Passive Radiator

Basic Theory

A passive radiator is used in conjunction with an active driver and its purpose is to replace the port or vent of a typical 4th order enclosure.  A passive radiator is sometimes referred to as a drone cone.  A passive radiator (PR) enclosure is most similar to a vented enclosure in that they acoustically behave very much the same.  Response characteristics include: there is a notch at the Fp of the passive radiator (resonant frequency of PR) and the typical cut-off rate below fB is 36 dB/octave.  The resonant frequency of the PR is intentionally altered by the designer in order to achieve the proper fB of the enclosure.  In other words, it is used to tune the box to the desired frequency and for optimum performance.  This is done my adding or removing calculated amounts of mass from the cone of the PR.  More mass = lower tuning.  Less mass = higher tuning.  The increases mass also helps to lower the Fp of the PR which in turn moves the undesired notch out of the passband resulting in improved transient response.  In theory, the Vd (volume displaced by PR) should be at least 2 times the Vd of the driver it is being used with.  Yet in practice, a good rule of thumb to go by is to have anywhere from 3-4 times as much displacement in the PR.  This is to ensure the longevity of the PR's by preventing excessive continual over-excursion. 
Advantages

Simplicity of tuning.  By merely adding and removing small amounts of mass, the tuning frequency of the enclosure may be changed up or down by as much as 15 Hz or as little as 0.1 Hz.  Precision tuning is very possible.  Ability to tune small enclosures to very low frequencies without the loss of volume due to internal ports taking up enormous amounts of precious space.   No port noise or any kind of air-turbulence of air speed levels to worry about.  Pipe resonances and port standing waves are non-existent because there are no ports or vents in this system.  Better driver stability below fB due to increased damping on the driver below fB.  This is because of specific compliance characteristics of the PR which help to keep the driver under better control at subsonic frequencies.
Disadvantages Steepest of all cut-off rates with a roll-off 36 dB/octave below fB.  Given the same size volume and tuning frequency of its vented counterpart, the PR alignment would result in a slightly higher f3.  The expense of of PR's can be quite high when compared to a simple piece of PVC pipe.  Especially when 2 or more PR's is needed, which is usually the case when using high-power, high-excursion drivers.
Best Applications Best suited just about anywhere a regular vented enclosure would be used.  May be used in applications where a smaller box is desired while wanting to maintain a 4th order alignment.  It was once believed that the PR alignment can be made half the volume of the same vented alignment and still be designed to have the same tuning frequency and achieve the same frequency response. Though this theory has been argued.  Passive Radiator alignments in most cases will require a comparable box volume and tuning as 4th order vented alignment in order to achieve similar results.

TL - Transmission Line
Contributed by m.bolech

Basic Theory

 

The driver is mounted in a type of acoustical labyrinth or long pipe commonly referred to as a transmission line.  The length of this transmission line is dependent upon the Fs of the driver.   This t-line may have a tapered effect or maintain the same cross-sectional area throughout its length and may also contain various folds which help reduce the overall size of the enclosure.  The length of the classic transmission line corresponds to the 1/4 wavelength of the resonant frequency of the driver.   The t-line is usually filled with various types of fluffy stuffing material (like polyester or wool) for damping higher order resonances. Further, the stuffing will make the acoustic wave-propagation more isothermal, which leads to a decrease in speed of sound through the t-line at higher frequencies (hundreds of Hz).  At the basic tuning frequency the effect of lowered speed of sound is negligible though, so that –alas- the required line length remains the same irrespective of stuffing density.

More information on methods and formulas for designing TL's can be found in publications of Augspurger [J. Audio Eng. Soc. 48, 424 (2000)] and King (quarter-wave.com).

 
Advantages Transient response is considered equal to or better than a 2nd order sealed enclosure and is considered far superior to that of a vented enclosure.  The cut-off rate is somewhat shallower than a typical sealed enclosure and may be as low as 10 dB/octave or lower.  This results in improved deep bass performance.  Less upper bass coloration due to reduced impedance peaks.  A cleaner, more pure, and deeper bass.
Disadvantages

 

Somewhat difficult to design as well as build.  Not all drivers will work well for a TL enclosures, although transmission lines can be made with many types of drivers.  Enclosure size may be very large.
Best Applications

 

Where you've got a ton of room, a ton of time, and a ton of patience.   TL's will work well basically wherever any of the other alignments would work.  Its unique performance characteristics make it suitable for even the most serious audiophile.

Compound or Isobaric - Dual Drivers
 

Basic Theory

Two drivers are mounted together in an enclosure with a cavity of air between the two drivers.  The drivers must operate in phase with each other.  The cavity of air between the drivers should be made as small as possible without compromising the operation of either driver.   The modeling for this type of enclosure is done just as you would any other speaker enclosure except you take the Vas of the driver and divide by 2.  This will in effect make all your speaker enclosures half as big as they would normally be for any particular driver.  
Advantages Improved sonic bass response.  Bass is claimed as being tighter, faster, more accurate and more pure.  Vas of the driver is cut in half.  The volume of enclosure required to obtain a specific frequency response can be achieved in only half the volume.  This is where isobaric enclosures have their biggest advantage.
Disadvantages Wasted amplifier power to driver the internal sub.  Efficiency of the system is down 3 dB as compared to a single driver due to the added cone mass and the reduced Vas.  When you compare isobarics to a system which houses two drivers each in their own enclosure, this system wis actually 6 dB less efficient.  
Best Applications Where size is a big issue.  When you want the box to be very small.  Where more accurate bass is more important than lots of bass.  If you have a hefty amplifier with plenty of juice to spare and a driver that can handle a good amount of power.   Suited for music, home theater and car.  Not used too often these days.

Push/Pull  - Dual Drivers

Basic Theory

Two drivers share an acoustic volume of air within a single enclosure.  The best way to take advantage of this alignment is to mount one driver facing outwards with the other driver inverted and facing inwards.  The drivers are then wired so that they are electrically out of phase while remaining mechanically still in phase with one another.  Odd ordered harmonics are cancelled out by using this approach according to Vance Dickason.  According to M&K who specialize is push/pull subwoofers claim that this approach cancels out even ordered harmonics.  So take your pick.  Either way, harmonic distortion is reduced in that any anomalies or variations in the two driver's spider, cone or suspension characteristics are canceled out by the other driver's inversely proportional anomalies and variations.  The sound is said to be as accurate and pure as it can possibly be with each driver "correcting" the other driver.   Optional designs include having the two drivers share the same acoustic volume of air while maintaining the more traditional look of having both drivers fire forward into the listening environment.   Though this does not have the same harmonic cancellation effect, all other characteristics between the two alignments is identical.  Box volume must be twice that of a single driver.  This can be easily modeled by taking the Vas of a single driver and multiplying it by two.  The system has an increased efficiency of 3dB over a single driver.  Power handling for the system is twice that of single driver.  Frequency response is the same for a single driver in an enclosure exactly half the size.
Advantages Increased output and power handling.  Very high SPL capability.
Disadvantages One single huge speaker enclosure that may be both unattractive, hard to build and hard to move.  Response it essentially identical to building two smaller enclosures of exactly half the size but without the versatility of placement of two separate subs.  There are no real disadvantages to building this kind of enclosure as the speakers will behave just as they would in enclosures by themselves.  It's very common to make MMT style speakers and use the two drivers in the same enclosure.
Best Applications

Where one sub just isn't enough.  High power high output applications.  If you choose to do the push/pull configuration, the sonic advantage may make this sub more suitable for audiophile music and critical listening experiences.

 
Disclaimer:  This page has been referenced by numerous sites over the years and has been, to my knowledge, a fairly useful resource for many DIY speaker builders such as myself.  I wrote most of this information back in 1999 when there the world wide web was more of a playground than the information super highway it has become. I have made little attempt over the years to correct or make more accurate anything I wrote way back then on this page. If you find something written here is in fact not true, I'd be happy to make a correction, just drop me an email. These theories are merely a short summary of different enclsoure types, concepts, ideas, articles, papers, and books that I've read (in addition to some of my own personal experience) on the subject of speaker enclosure design. By no means does this represent a complete or completely accurate portrayal of all enclosure theories, pros and cons or best applications.  I put this out there as my opinion only. Use this information at your own risk!   Thanks. DM.


Copyright 1999-2005 © Audio Innovation, Inc.  All Rights Reserved.
This page last updated on November 01, 2014.

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